The nation’s top military officer Wednesday declared the security situation in Iraq “remarkably better,” so good in fact that he expects to recommend more U.S. troop reductions this fall if conditions hold.

Just back from a tour of two war fronts - Iraq and the Afghanistan-Pakistan region - Adm. Michael G. Mullen said he expected to witness improvements in Baghdad and across Iraq, but was surprised by how well a 17-month-old U.S. troop surge has worked.

“I won’t go so far as to say that progress in Iraq, from a military perspective, has reached a tipping point or it is irreversible,” Adm. Mullen, the Joint Chiefs chairman, said at a press conference with Defense Secretary Robert M. Gates. “But security is unquestionably and remarkably better.”

The last of five reinforcement combat brigades have left Iraq, leaving behind 15 such units. Gen. David H. Petraeus, the top commander in Iraq, a key architect of the February 2007 surge and recently confirmed by the Senate to lead U.S. Central Command, has called for several months of assessment before deciding whether to reduce troop levels below about 145,000.

But Adm. Mullen’s statement that “I expect to be able early in the fall to recommend to the secretary and to the president further troop reductions” is a clear signal that top commanders in Iraq think a continued drawdown is warranted.

The two most important questions in the equation are: Can the Iraqi Security Forces inherit and win the fight, and is the insurgency nearly defeated?

Last week, Iraqi Prime Minister Nouri al-Maliki declared that his country had defeated al Qaeda in Iraq, the Osama bin Laden terrorist franchise that at one time controlled much of Anbar province west of Baghdad and sent suicide bombers to the capital at will.

The administration now reports that violence in Iraq has plummeted from 1,400 incidents a week to fewer than 400 nationwide.

Adm. Mullen was not so optimistic about the war in Afghanistan, saying commanders there pressed him to supply more U.S. troops to reinforce the 32,000 already present. Taliban forces last week were able to execute a daring sophisticated attack on a U.S. outpost in Wanat that killed nine American service members.

“It’s a tougher fight. It’s a more complex fight,” he said. “They need more troops to have the long-term impact.”

Mr. Gates said the Pentagon is studying ways to send reinforcements, but Adm. Mullen previously said that no additional troops are available for Afghanistan until Iraq supplies more of its own.

Adm. Mullen and Mr. Gates said Pakistan has failed to stem the flow of fighters recruited and trained in unregulated tribal areas.

“We’re seeing a greater number of insurgents and foreign fighters flowing across the border with Pakistan, unmolested and unhindered,” Adm. Mullen said. “This movement needs to stop.”

The Joint Chiefs chairman said the administration is trying to persuade Pakistanis to take action by impressing on them the internal threat they face from militants and al Qaeda terrorists operating in the tribal areas.

“We see this threat accelerating,” he said. “We see it almost becoming a syndicate of different groups who heretofore had not worked closely together.”

The new Pakistani civilian government pledged to tighten the border. But after launching several operations earlier in the month, it also talked of negotiating with militant tribal leaders instead of fighting them. The U.S. says such agreements in the past produced nothing.

“There is no question that the absence of pressure on the Pakistani side of the border is creating an opportunity for more people to cross the border and launch attacks,” Mr. Gates said.

Still, the admiral spoke of progress he tracked in southern Afghanistan, the birthplace of the Taliban’s harsh Islamist rule. Marines and Army soldiers have liberated villages and trained Afghan forces to hold them. “Clearly, we have a long way to go but we are making strides,” Adm. Mullen said.

The Pentagon sent 3,500 Marines into southern Afghanistan in the spring to stem a Taliban offensive. The unit is scheduled to leave in November.